Mock Quiz Hub

Recent Updates

Added: OS Mid 1 Quiz

Added: OS Mid 2 Quiz

Added: OS Lab 1 Quiz

Check back for more updates!

Time: 00:00

Quiz

Navigate through questions using the controls below

0%

Question 1 of 40 Quiz ID: q1

What is the Laplace transform of the function f(t) = t^3 * e^(4t)?

3! / (s-4)^4

6 / (s-4)^4

3! / s^4

6 / s^4

Question 2 of 40 Quiz ID: q2

Which theorem states that L{e^(at)f(t)} = F(s-a) where F(s) = L{f(t)}?

Linearity Theorem

First Shifting Theorem (S-Shifting)

Second Shifting Theorem (T-Shifting)

Convolution Theorem

Question 3 of 40 Quiz ID: q3

What is the Laplace transform of the Dirac delta function δ(t-5)?

1

e^(-5s)

e^(5s)

5/s

Question 4 of 40 Quiz ID: q4

If L{f(t)} = F(s), what is L{t^2 * f(t)}?

F''(s)

-F''(s)

(-1)^2 * d²F(s)/ds²

d²F(s)/ds²

Question 5 of 40 Quiz ID: q5

The Laplace transform of the derivative y'(t) is given by:

sY(s) - y(0)

sY(s) + y(0)

Y(s)/s - y(0)

s^2Y(s) - sy(0) - y'(0)

Question 6 of 40 Quiz ID: q6

What is the inverse Laplace transform of F(s) = e^(-7s) * s/(s^2+4)?

cos(2t) * u(t-7)

cos(2(t-7)) * u(t-7)

sin(2(t-7)) * u(t-7)

cos(2t-7)

Question 7 of 40 Quiz ID: q7

The convolution of two functions f(t) and g(t) is defined as:

∫₀ᵗ f(τ)g(τ) dτ

∫₀ᵗ f(t-τ)g(τ) dτ

∫₀ᵗ f(τ)g(t-τ) dτ

∫₀ᵗ f(t)g(t-τ) dτ

Question 8 of 40 Quiz ID: q8

According to the Convolution Theorem:

L{f(t)g(t)} = L{f(t)} * L{g(t)}

L{f(t) * g(t)} = L{f(t)} + L{g(t)}

L{f(t) * g(t)} = L{f(t)} L{g(t)}

L{f(t)/g(t)} = L{f(t)} / L{g(t)}

Question 9 of 40 Quiz ID: q9

For a periodic function f(t) with period T, the Laplace transform is given by:

L{f(t)} = (1/(1-e^{-sT})) ∫₀ᵀ e^{-st} f(t) dt

L{f(t)} = ∫₀ᵀ e^{-st} f(t) dt

L{f(t)} = (1/(1-e^{sT})) ∫₀ᵀ e^{-st} f(t) dt

L{f(t)} = ∫₀∞ e^{-st} f(t) dt / T

Question 10 of 40 Quiz ID: q10

The unit step function u(t-a) is defined as:

0 for t < a, 1 for t ≥ a

1 for t < a, 0 for t ≥ a

a for t < 0, 1 for t ≥ 0

1 for all t

Question 11 of 40 Quiz ID: q11

What is the Laplace transform of the function g(t) = ∫₀ᵗ sin(3τ) dτ?

3 / [s(s^2+9)]

1 / [s(s^2+9)]

3 / (s^2+9)

s / (s^2+9)

Question 12 of 40 Quiz ID: q12

To solve an ODE using Laplace transforms, the initial conditions are incorporated:

After finding the inverse Laplace transform

During the transformation of the derivatives

They are not needed for the Laplace transform method

By solving a separate algebraic system

Question 13 of 40 Quiz ID: q13

The function f(t) = { -1 if 0≤t<2, 1 if 2≤t } can be expressed using the unit step function as:

-1 + 2u(t-2)

1 - 2u(t-2)

-u(t-2) + 2

u(t-2) - 1

Question 14 of 40 Quiz ID: q14

What is the Laplace transform of f(t) = e^(-3t) * cos²(t)? (Hint: Use a trigonometric identity)

1/(2(s+3)) + (s+3)/(2[(s+3)^2+4])

s/(s^2+1) * 1/(s+3)

(s+3)/((s+3)^2+1)

1/(s+3) + 1/((s+3)^2+1)

Question 15 of 40 Quiz ID: q15

If L^{-1}{F(s)} = f(t), what is L^{-1}{F(s+5)}?

e^(5t) f(t)

e^(-5t) f(t)

f(t-5) u(t-5)

f(t+5)

Question 16 of 40 Quiz ID: q16

The Dirac delta function δ(t) is best described as:

A classical function with infinite value at t=0

A distribution or generalized function

The derivative of the unit step function u(t)

Both B and C

Question 17 of 40 Quiz ID: q17

For the function f(t) = t * cosh(at), which method is most efficient for finding its Laplace transform?

Definition (direct integration)

First Shifting Theorem

Derivative of the Transform Theorem (Multiplication by t)

Convolution Theorem

Question 18 of 40 Quiz ID: q18

The solution to the IVP y'' - 5y' + 6y = 0, y(0)=2, y'(0)=3 using Laplace transforms involves solving:

(s²Y - 2s - 3) - 5(sY - 2) + 6Y = 0

(s²Y - 2s - 3) - 5(sY) + 6Y = 0

s²Y - 5sY + 6Y = 0

(s²Y - 2s) - 5(sY - 3) + 6Y = 0

Question 19 of 40 Quiz ID: q19

The s-domain algebraic equation for the circuit L di/dt + iR + (1/C)∫i dx = v(t) involves the term for the integral. Its Laplace transform is:

I(s)/s

s I(s)

I(s) / (Cs)

I(s) / (sC)

Question 20 of 40 Quiz ID: q20

What is the inverse Laplace transform of F(s) = 1 / [s(s+3)]?

(1/3)(1 - e^(-3t))

e^(-3t) - 1

(1/3)(e^(-3t) - 1)

1 - e^(-3t)

Question 21 of 40 Quiz ID: q21

The Laplace transform of the function f(t) = sin(3t) / t is found using which theorem?

First Shifting Theorem

Multiplication by t^n

Division by t

Convolution Theorem

Question 22 of 40 Quiz ID: q22

The function |sin(t)| is periodic. What is its period?

π

2π

π/2

4π

Question 23 of 40 Quiz ID: q23

The property ∫_{-∞}^{∞} f(x) δ(x-a) dx = f(a) is known as:

The definition of the delta function

The sifting property

The sampling property

Both B and C

Question 24 of 40 Quiz ID: q24

To find L{u(t-2) * t²}, we must first:

Directly apply the definition

Express t² in terms of (t-2)

Use the convolution theorem

Use the derivative property

Question 25 of 40 Quiz ID: q25

The inverse Laplace transform of F(s) = 3! / (s-2)^4 is:

e^(2t) * t^3

e^(2t) * t^4

e^(2t) * t^3 / 3!

t^3 / 3!

Question 26 of 40 Quiz ID: q26

A system of differential equations is solved by Laplace transforms by:

Solving each equation completely separately

Transforming each equation and solving the resulting system of algebraic equations simultaneously

Adding the equations together first

Taking the inverse transform before solving algebraically

Question 27 of 40 Quiz ID: q27

The function h(t) in an LTI system such that y(t)=x(t)*h(t) is called the:

Input function

Output function

Impulse response

Transfer function

Question 28 of 40 Quiz ID: q28

The Laplace transform of the integral equation y(t) = 1 - sin(t) - ∫₀ᵗ y(τ)dτ, y(0)=0, becomes:

Y(s) = 1/s - 1/(s²+1) - Y(s)/s

Y(s) = 1/s - 1/(s²+1) - sY(s)

Y(s) = s - s/(s²+1) - Y(s)

Y(s) = 1 - 1/(s²+1) - Y(s)/s

Question 29 of 40 Quiz ID: q29

The function f(t) = e^(5t) * sin(2t)/t requires which combination of theorems for finding its Laplace transform?

First Shifting and Division by t

First Shifting and Convolution

Division by t and Convolution

Second Shifting and Multiplication by t

Question 30 of 40 Quiz ID: q30

The main reason Laplace transforms are effective for solving linear ODEs with constant coefficients is that they:

Turn differentiation into multiplication

Work for any nonlinearity

Always yield simpler integrals than other methods

Eliminate the need for initial conditions

Question 31 of 40 Quiz ID: q31

What is the correct Laplace transform expression for the second derivative y''(t)?

s² Y(s)

s² Y(s) - y'(0)

s² Y(s) - s y(0) - y'(0)

s Y(s) - y(0)

Question 32 of 40 Quiz ID: q32

The inverse Laplace transform of F(s) = e^{-7s} / [(s-5)² + 4] is:

(1/2) e^(5(t-7)) sin(2(t-7)) u(t-7)

e^(5(t-7)) sin(2(t-7)) u(t-7)

(1/2) e^(5t) sin(2t) u(t-7)

e^(5t) sin(2(t-7)) u(t-7)

Question 33 of 40 Quiz ID: q33

For the function f(t) = t² * cos(at), finding its Laplace transform directly by integration would be:

Simple using a standard integral

Very difficult due to the t² term

Easier than using theorems

Impossible

Question 34 of 40 Quiz ID: q34

The function defined by the limit of δ_n(x) = { n for -1/(2n) ≤ x ≤ 1/(2n), 0 otherwise } as n→∞ is:

The Gaussian function

The Dirac delta function

The Unit step function

The Sinc function

Question 35 of 40 Quiz ID: q35

The Convolution Theorem is particularly useful for finding:

The Laplace transform of a product f(t)g(t)

The inverse Laplace transform of a product F(s)G(s)

The Laplace transform of a sum f(t)+g(t)

The inverse Laplace transform of a sum F(s)+G(s)

Question 36 of 40 Quiz ID: q36

In the solution process using Laplace transforms, the step after transforming the ODE into an algebraic equation is:

Apply initial conditions

Solve the algebraic equation for Y(s)

Take the inverse Laplace transform

Simplify the expression

Question 37 of 40 Quiz ID: q37

The Laplace transform H(s) = Y(s)/X(s) for an LTI system is called the:

Impulse response

Step response

Transfer function

Characteristic equation

Question 38 of 40 Quiz ID: q38

The function f(t) = { t-1 if 1≤t<2, 3-t if 2≤t<3 } can be expressed using unit step functions as:

(t-1)[u(t-1)-u(t-2)] + (3-t)[u(t-2)-u(t-3)]

(t-1)u(t-1) + (4-2t)u(t-2) + (t-3)u(t-3)

(t-1)u(t-1) + (3-t)u(t-2)

u(t-1)(t-1) + u(t-2)(3-t)

Question 39 of 40 Quiz ID: q39

The stability of a system described by a transfer function H(s) can often be analyzed by examining:

The zeros of H(s)

The poles of H(s)

The gain of H(s)

The order of the numerator of H(s)

Question 40 of 40 Quiz ID: q40

When applying the Laplace transform method to a differential equation, the final solution in the time domain is valid:

Only for t > 0

For all real t

Only at the initial condition t=0

Only for t < 0

Quiz Summary

Review your answers before submitting

40

Total Questions

0

Answered

40

Remaining

00:00

Time Spent

Question 1 of 40

!

Quiz

Quiz Summary

Confirm Submission